Distances, such as lengths, widths, and thicknesses, are commonly measured with rulers. FIG. 1 illustrates an example of how ruler 20 is used to measure length L of elongated object 22. Ruler 20 is positioned parallel to the length of object 22. The value of length L is then approximately the difference between the ruler distance markings opposite the longitudinal ends of object 22. Measuring length L is simplified when one longitudinal end of object 22 is opposite the zero-distance marking on ruler 20. In that case, the value of length L is approximately the value of the ruler distance marking opposite the other longitudinal end of object 20.
Angles are commonly measured with protractors. FIGS. 2a and 2b illustrate how manual protractor 30 is used to measure angle α formed by a pair of straight lines 32 that meet at angle vertex 34. Vertex 36 of protractor 30 is placed at angle vertex 34. The value of angle α is then approximately the difference between the protractor angular markings through which lines 32 pass. Similar to how measuring length L is simplified, measuring angle α is simplified when one of lines 32 passes through one of the zero-angular markings on protractor 30. The value of angle α is then the value of the protractor angular marking through which the other of lines 32 passes.
Another type of protractor is electronic protractor 40 as shown in FIG. 3. Electronic protractor is formed with two straight legs 42 hingeably connected at pivot 44. Angle α is measured with protractor 40 by placing it over angle α so that legs 42 are respectively aligned with lines 32 that define angle α. The center 46 of pivot 44 overlies angle vertex 34. Video display 48 on one of legs 42 provides the value of angle α.
Situations arise in which it is desirable to measure a distance or an angle but no ruler or protractor is readily available to measure the distance of angle. Situations also arise in which it would be difficult to measure a distance or an angle with a ruler or protractor even if a ruler or protractor were readily available. For instance, the distance or angle may be of such a nature that a ruler or protractor cannot be readily aligned to the distance or angle in the way needed to make the measurement.
Mobile information-presentation devices having video-imaging and mathematics-computation capabilities are in common use. As an example of such a device, FIG. 4 illustrates calculator 50 having video screen 52 for presenting the results of calculations performed by entering data via keyboard 54. Calculator 50 provides various trigonometric functions such as sine, cosine, and tangent as well as hyperbolic functions such as inverse sine (sin−1), inverse cosine (cos−1), and inverse tangent (tan−1). By appropriate programming of calculator 50, screen 52 can often illustrate curves of various mathematical functions.
A substantial percentage of people are more likely to have ready access to mobile information-presentation devices having video-imaging and mathematics-computation capabilities than to rulers and protractors, especially protractors. In light of this, it would be desirable for a mobile information-presentation device having video-imaging and mathematics-computation capabilities to also have the capability to perform various measurements, including measuring angle and lines.